Florence stands in her backyard and admires her flower gardens. First, she looks to her rose garden. Her rose garden is 80 feet away from her. She turns 63° and views where she has lilies planted. The lily garden is 140 feet away from her. How far apart are the rose garden and the lily garden?

The rose garden is 125.82 feet apart from the lily garden.

Step-by-step explanation:

See the attached diagram.

The position of Florence is A and the position of the rose garden and the lily garden forms a triangle Δ ARL.

Now, from the property of triangle, we can write

x² = 80² + 140² - 2 × 140 × 80 × Cos 63°

⇒ x² = 15830.61

⇒ x = 125.82 feet.

Therefore, the rose garden is 125.82 feet apart from the lily garden. (Answer)

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